The director of the British Museum says he is stepping down with immediate effect after admitting to failings in the museum's investigation into the theft of items from its collection.

Hartwig Fischer, a German art historian who was due to leave his post next year, said that the museum did not sufficiently respond to warnings that an employee may have been stealing items and the failings "must ultimately rest" with him.

"It is evident that the British Museum did not respond as comprehensively as it should have," he said in a statement.

The British Museum, among the most visited in the world and one of London's most popular tourist attractions, said last week a member of staff had been dismissed after items including gold jewellery and gems dating from the 15th century BC to the 19th century AD, had been found stolen from a storeroom.

Police said on Thursday said they had interviewed but not charged an unnamed man over the stolen artefacts.

Fischer said that he withdrew remarks made about the art dealer who first alerted museum bosses to the stolen items.

He expressed "sincere regret" over the "misjudged" comments.

Earlier this week, Fischer said Ittai Gradel, an antiquities dealer, withheld information about the scale of the stolen items when he contacted the museum.

The museum's board of trustees, chaired by former United Kingdom finance minister George Osborne, accepted Fischer's resignation.

"I am clear about this: we are going to fix what has gone wrong," Osborne said.

"The museum has a mission that lasts across generations. We will learn, restore confidence and deserve to be admired once again."